### Video Transcript

How many real roots does the equation ππ₯ squared plus ππ₯ plus π equals zero have if π is not equal to zero and π squared minus four ππ is equal to zero?

Well, this equation is the general form of a quadratic equation. And hopefully, you can recall that if ππ₯ squared plus ππ₯ plus π equals zero, then π₯ is equal to the negative of π plus or minus the square root of π squared minus four ππ all over two π. Now obviously, this only works if π is not equal to zero. Otherwise, weβd be dividing something through it by zero. And they tell us that π is not equal to zero in the question, so thatβs good. And the other bit of information they give us is that π squared minus four ππ is equal to zero.

Now the value of π squared minus four ππ has a special name; we call it the discriminant. And itβs important because itβs the expression under the square root in this formula. And weβre told that in this particular case, that is equal to zero. So this means that the root of the equation, the possible values of π₯, are the negative value of the π coefficient plus or minus the square root of zero all over two times the value of the π coefficient. Mostly, the square root of zero is zero. So weβve got the negative value of π plus zero or minus zero, thatβs only one possible number, all over two π. So negative π plus zero or negative π minus zero. And whether you add zero or subtract zero, it doesnβt make any difference. You are just gonna get a value of negative π on the numerator, and youβre gonna get two expressions that look the same, negative π over two π in both cases.

So our formula gives rise in its two various forms to just the same one solution. So under the conditions given in the question, the answer is that there is only one real root.